Endogenous Second Moments: A Unified Approach to Fluctuations in Risk, Dispersion, and Uncertainty
40 Pages Posted: 20 Jun 2016 Last revised: 10 Mar 2018
Date Written: March 7, 2018
Many important statistics in macroeconomics and finance — such as cross-sectional dispersions, risk, volatility, or uncertainty — are second moments. In this paper, we explore a mechanism by which second moments naturally and endogenously fluctuate over time as nonlinear transformations of fundamentals. Specifically, we provide general results that characterize second moments of transformed random variables when the underlying fundamentals are subject to distributional shifts that affect their means, but not their variances. We illustrate the usefulness of our results with a series of applications to (1) the cyclicality of the cross-sectional dispersions of macroeconomic variables, (2) the dispersion of MRPKs, (3) security pricing, and (4) endogenous uncertainty in Bayesian inference problems.
Keywords: Cross-Sectional Dispersion, Endogenous Uncertainty, Nonlinear Transformations, Risk, Second Moments, Volatility
JEL Classification: C19, D83, E32, G13
Suggested Citation: Suggested Citation